Summary: 12322 J. Am. Chem. SOC.1993, 115, 12322-12329
Chiral Discrimination in Solutions and in Langmuir
Monolayers
David Andelman'*+and Henri Orland**$
Contributionfrom the School of Physics and Astronomy, Raymond and Beverly Sackler Faculty
of Exact Sciences, Tel Aviv University, Ramat Aviv 69978, Tel Aviv, Israel, Service de Physique
Thhorique, CE-Saclay, F-91191 Gif-sur-Yvette Cedex, France, and Groupe de Physique
Statistique, UniversitL de Cergy-Pontoise, BP 8428, 95806 Cergy-Pontoise Cedex, France
Received July 12, 1993"
Abstract: Inthis paper we examine theoretically the chiral discriminationof molecules with a single chiral center. We
propose a definition of the chiral discrimination parameter A in terms of the difference between the second virial
coefficient of pure enantiomers and their racemic mixture. This parameter enters in the equation of state of racemic
mixturesand willdetermine their phasediagrams. Wecalculate then thechiral discrimination between D-and L-alanine
using a Monte Carlosimulation to averageover 11 molecular degreesof freedom at fixed intermoleculardistances using
the CHARMM energy function. The discrimination is found to slightly favor homochirality and mainly comes from
sterichindrance at short distances. We also perform a direct integration for rigid chiral tetrahedron-shaped molecules.
Here there are only five rotational degreesof freedom. For a Lennard-Jones potential,the overall chiral discrimination
is found to be predominantly heterochiral. One of our main observations is that the pair free energy, internal energy,
and entropy differences between the two enantiomers may change signs as a function of the interpair distance. We
find that homochirality is preferred at shorter distances whereas heterochirality is favored at larger distances. With